[Music]

Narrator: A mortgage is a loan to purchase a house.

Mortgages are long-term obligations.

Most mortgages are loaned for a thirty-year period.

Every mortgage consists of several key pieces of data:

the loan amount, the interest rate, and the number of

payment periods.

The loan amount is the amount of money the bank lends you to

purchase the house.

This is the money you will pay back to the bank.

The interest rate is the additional amount of money you

will pay to the bank for borrowing the money.

The interest is what the bank earns for lending you

the money.

The number of payment periods is the number of months the

bank gives you to pay back the loan.

Let's look at some examples.

This table shows a thirty-year loan for the amount of one

hundred thousand dollars.

This is the loan amount.

The interest that the bank is charging you is five point

two-five percent.

The payment period is three hundred and sixty months, or

thirty years.

Using these three pieces of data you can construct an

amortization table, which is the schedule of payments to

repay the loan.

Let's use the TI-Nspire to do this.

Turn on the TI-Nspire.

Create a new document.

Decide if you want to save your document.

Create a spreadsheet window.

Input the following text labels into cells A1, A2, A3,

and A4.

Then input the following values in the corresponding

cells of column B.

We will be calculating the monthly mortgage payment for a

thirty-year mortgage of one hundred thousand dollars paid

at an interest rate of five point two five percent.

In cell B4 you will be using one of the Nspire's finance

functions to calculate the monthly payment.

The time value of money function takes the value from

cells B1 to B3 to calculate the monthly mortgage payment.

Input the first payment of the function as shown.

The time value function evaluates six numbers.

The first is the total number of payments.

So after the left parenthesis input cell reference B3.

The next value is the interest rate.

So after the comma input cell reference B2.

The next value is the loan amount, so after the comma

input cell reference B1.

The next reference is the future value of the mortgage.

Since you intend to pay the entire mortgage the future

value is zero.

So after the comma input zero.

The next two values are the number of payments per year

and the number of times the interest on the loan

is compounded.

In both cases assuming monthly amount.

So after the comma input twelve two times.

Complete the formula and press ENTER.

The time value function shows that the monthly mortgage

amount is about five hundred and fifty two dollars per

month for three hundred and sixty months.

To find out how much money you actually pay input the

following into cells A5 and B5.

You'll see that a one hundred thousand dollar loan paid over

thirty years cost nearly two hundred thousand dollars at a

loan interest rate of five point two five percent.

Suppose that the interest rate went down to five percent.

How does this affect the loan?

Change the value in cell B2.

Press ENTER.

A small change in the interest rate will result in several

thousand dollars worth of savings over the life of

the loan.

Now you can see why even minor changes in the interest rate

are important.

And this provides the first clue about what may have

occurred in the mortgage crisis.

But there's more.

Although every month the mortgage is the same

throughout the life of the loan, the amount that goes

towards paying back the one hundred thousand dollars, and

the amount that goes toward paying the interest on the

loan varies from month to month.

To see how this month-to-month payback works lets create an

amortization table.

What we want to keep track of are three things: the monthly

balance- how much is still left to pay on the loan, the

amount paid toward the principle, which the one

hundred thousand dollars borrowed, and the amount paid

toward interest.

Use the nav pad to restore the five point two five percent

interest in cell B2.

Move the cursor to the top of column C.

Input the column heading "balance".

The cursor is now in the gray cell where you can add

formulas to generate data.

We want to generate a sequence of numbers that reflects the

changes in the loan balance.

Since every month you pay five hundred and fifty-two dollars

you reduce the loan amount by this payment, but every month

you need to pay interest on the balance of the loan so we

need a formula that reflects this.

Let P represent the previous month's balance.

Our equation then changes to this.

The interest rate is divided by twelve because we are

calculating the monthly payment.

The five hundred and fifty-two represents the

mortgage payment.

Using the interest rate of five point two five percent

the equation changes to this.

We can generate the sequence of numbers representing the

loan balance during the three hundred and sixty months of

the repayment.

Press control and MENU and select generate sequence.

At the dialog box input this formula.

The term u(n-1) represents the previous term

in the sequence.

The cell references B2 and B4 are for the interest rate and

the monthly payment.

Press TAB to go to the next cell.

Here you add the initial value, which is the original

amount of the loan, or one hundred thousand dollars.

Press TAB and set the number of terms in the sequence as

three hundred and sixty, which is the number of

loan payments.

Keep pressing TAB to get to the OK button and press ENTER.

If you scroll down you will see the complete list of three

hundred and sixty terms representing the monthly

balance for the mortgage.

Now move the cursor so that it is at the very top of

column D.

Add this label.

Press ENTER.

The cursor is now on a cell there you can write a formula

to generate data.

You want to generate the interest payment made

each month.

This means multiplying the current loan balance by the

monthly interest.

Input this formula and press ENTER.

This generates a sequence of three hundred and sixty terms

that represent the monthly interest payment.

Now move the cursor so that it is at the very top of

column D.

Add this label.

Press ENTER.

This column will track the monthly payment on the

principle of the loan, the one hundred thousand dollars.

Input this formula and press ENTER.

We now have a complete amortization table for

the loan.

The first thing to notice is that at the beginning most of

your mortgage payment goes toward interest, not

the principle.

This becomes clear by looking at a SCATTER PLOT of columns

D and E.

Press HOME to create a graph window.

Press MENU, and under GRAPH TYPE select SCATTER PLOT.

Move the cursor to the drop-down MENU for x.

Select PRINCIPLE.

Press TAB to highlight the y drop-down MENU.

Select INTEREST.

To see the data press MENU and under the WINDOW option select

ZOOM DATA.

You'll see a scatter plot of interest versus

principle payments.

At the start of the loan most of your payment is

toward interest.

It's only until the two hundred and third payment, or

nearly seventeen years, that most of the monthly mortgage

payment goes toward the principle.

If you input a higher interest rate you'll see that it takes

even longer before you reach the point where most of the

payment goes toward the principle.

As you begin to pay down the principal you gain what is

called equity on the house.

Equity is the portion of the loan that you have paid back.

Think of it as the portion of the house that you own.

To see how equity grows let's use the cumulative

sum formula.

GO to the top of column F and add the label "equity".

Use the cumulative sum formula for column F.

Scroll down the equity column.

You'll see that it takes two hundred and forty-five

payments before you have made half the principle.

In other words it will take twenty-one years before half

of the mortgage is fully paid.

During this time the value of the house will likely go up.

Suppose that this one hundred thousand dollar house gains

five percent in value every year.

The total equity is the sum of the increased value of the

house and the total amount of principle you have paid back.

So buying a house is a long-term commitment.

When a bank lends money for a mortgage the expectation is

that the person buying the house has the commitment to

pay the loan.

Even though it takes a long time to pay it back there is

also the benefit of having the house gain in value so that

the total equity on the house continues to increase.

During the mortgage crisis of 2008 neither of these

assumptions turned out to be true.

Many people stopped paying their mortgage and the value

of houses began to go down.

Now that you know how to calculate a mortgage we can

begin to analyze what went wrong during the

mortgage crisis.

Be sure to save the amortization template

you created.

Call the file "amort".